CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is :


A

1.5 R

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

2.5 R

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

4.5 R

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

7.5 R

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

7.5 R


Let m1=M and m2=5M

Let centre of mass C at a distance x1 from m1 and x2 from m2.

m1x1=m2x2Mx1=5Mx2x1=5x2 and x1+x2=12R5x2+x2=12R6x2=12Rx2=2Rx1=10R

Since the masses are moving under mutual attraction the position of centre of mass remains constant.

When the masses are in contact, let x1 and x2 be the distance of their centres from the centre of mass.

m2x1=m2x2Mx1=5Mx2x1=5x2Also x1+x2=3R5x2+x2=3R6x2=3Rx2=0.5R and x1=2.5R

Hence the distance travelled by the smaller mass is

x1 –x1’ = 10R – 2.5R = 7.5R


flag
Suggest Corrections
thumbs-up
4
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Gravitation Field
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon